A) \[\left( \frac{9}{2},4 \right)\]
B) \[\left( \frac{19}{2},6 \right)\]
C) \[\left( \frac{11}{2},\frac{11}{2} \right)\]
D) \[\left( 8,\frac{13}{2} \right)\]
Correct Answer: B
Solution :
Since, D is the mid point of BC. So, coordinate Of BC are \[\left( \frac{{{x}_{2}}+{{x}_{3}}}{2},\frac{{{y}_{2}}+{{y}_{3}}}{2} \right)\] Given, \[G(7,5)\] is the centroid of \[\Delta ABC\] \[\therefore \] \[7=\frac{2+{{x}_{2}}+{{x}_{3}}}{3}\] and \[5=\frac{3+{{y}_{2}}+{{y}_{3}}}{3}\] \[\Rightarrow \] \[{{x}_{2}}+{{x}_{3}}=21-2\] and \[{{y}_{2}}+{{y}_{3}}=15-3\] \[\Rightarrow \] \[{{x}_{2}}+{{x}_{3}}=19\] and \[{{y}_{2}}+{{y}_{3}}=12\] \[\Rightarrow \] \[\frac{{{x}_{2}}+{{x}_{3}}}{2}=\frac{19}{2}\] and \[\frac{{{y}_{2}}+{{y}_{3}}}{2}=6\] \[\therefore \] Coordinate of D are \[\left( \frac{19}{2},6 \right)\]You need to login to perform this action.
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